There were some cosmetic differences between the "Indian" and the Royal Enfield models that they were derived from.
Different wheel sizes, different emblems and trim items, and even some things like fenders. This was part of giving it the "Indian" look, even though it was a Royal Enfield bike.
So, probably that was what comprised the "assembly in the US" part of it.
The truth is that the "Indian" contract is what became the "bread and butter" for Royal Enfield, and when the Indian contract expired, Royal Enfield fell on hard times, and then sold the company to AMC around 1960, who subsequently sold it again to somebody else in around 1962.
After that, only Interceptors and some little bikes like the Crusader and Continental were produced until about 1965, and all other models were deleted.
They managed to make Interceptors for the remainder of the 1960s, and then closed the doors permanently in 1970.
So really, it was the termination of the contract with Indian that pretty much spelled the end for RE. But, they still managed to hang on for another decade, and produced some very nice motorcycles, until they finally couldn't hang in there any longer.
The competition from Triumph, BSA, and Norton was very stiff during the 1960s, and even though the Interceptor was superior in alot of ways, the other marques had the "charisma" and were more popular sellers.
When the Honda 750-4 was introduced in 1969, that was the beginning of the end for the entire British motorcycle industry.